Study guide for AP test on TOPIC 1 Matter & Measurementtoolbox1.s3-website-us-west-2.amazonaws.com/site_0303/Lassiter_… · (b) Express the measurement 6.0 310 m using a prefix to

Copyright ©2009 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

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Chemistry: The Central Science, Eleventh Edition

By Theodore E. Brown, H. Eugene LeMay, Bruce E. Bursten, and Catherine J. Murphy

With contributions from Patrick Woodward

Study guide for AP test on TOPIC 1 Matter &

Measurement

The following list is a GUIDE to what you should study in

order to be prepared for the AP test on TOPIC 1

ALL students should:

• Recall a definition of chemistry

• Understand the process and stages of scientific (logical) problem

solving

• Recall the three states of matter, their general properties and the

methods for their interconversion

• Understand and recall definitions for physical and chemical change







• Know the difference between elements, mixtures and compounds including the difference between heterogeneous and homogeneous mixtures

• Understand and be able to use scientific notation (standard form) Recall and use SI units and prefixes

• Be able to convert between units

• Understand the concept of derived units and use relationships relating to density

• Recall the meaning of uncertainty and understand and be able to use the rules for determining significant figures and rounding off

• Understand the differences between, and be able to apply, the concepts of accuracy and precision

• Learn, and be able to use, formulae for the conversion of the three different temperature units studied in TOPIC 1

• Learn and be able to apply the formula for percentage error







Classification of Matter figure 1.9

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Sample Exercise 1.1 Distinguishing Among Elements, Compounds, and Mixtures

“White gold,” used in jewelry, contains gold and another “white” metal such as palladium. Two different

samples of white gold differ in the relative amounts of gold and palladium that they contain. Both samples are

uniform in composition throughout. Without knowing any more about the materials, classify white gold.

Aspirin is composed of 60.0% carbon, 4.5% hydrogen, and 35.5% oxygen by mass, regardless of its source.

Use Figure 1.9 to characterize and classify aspirin.

Answer:

Practice Exercise 1.1

Solution

Because the material is uniform throughout, it is homogeneous. Because its composition differs for the two

samples, it cannot be a compound. Instead, it must be a homogeneous mixture.







Metric System

Prefixes convert the base units into units that

are appropriate for the item being measured.

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Hall, Inc.







Sample Exercise 1.2 Using Metric Prefixes

What is the name given to the unit that equals (a) 10-9 gram, (b) 10-6 second, (c) 10-3 meter?

(a) What decimal fraction of a second is a picosecond, ps? (b) Express the measurement 6.0 103m using a

prefix to replace the power of ten. (c) Use exponential notation to express 3.76 mg in grams. Answer:


Solution

In each case we can refer to Table 1.5, finding the prefix related to each of the decimal fractions: (a)

nanogram, ng, (b) microsecond, s, (c) millimeter, mm.







Temperature

By definition

temperature is a

measure of the

average kinetic

energy of the

particles in a sample.

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Temperature

• The Kelvin is the SI

unit of temperature.

• It is based on the

properties of gases.

• There are no

negative Kelvin

temperatures.

• K = C + 273.15

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Temperature

• The Fahrenheit scale

is not used in

scientific

measurements.

• F = 9/5(C) + 32

• C = 5/9(F − 32)

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Hall, Inc.







Sample Exercise 1.3 Converting Units of Temperature

If a weather forecaster predicts that the temperature for the day will reach 31 °C, what is the predicted

temperature (a) in K, (b) in °F?

Ethylene glycol, the major ingredient in antifreeze, freezes at –11.5ºF . What is the freezing point in (a) K,

(b) °F? Answer:


Solution







Density

Density is a physical property of a substance.

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d = m

V







(a) Calculate the density of mercury if 1.00 102 g occupies a volume of 7.36 cm3. (b) Calculate the volume

of 65.0 g of the liquid methanol (wood alcohol) if its density is 0.791 g/mL. (c) What is the mass in grams of

a cube of gold (density = 19.32 g/cm3) if the length of the cube is 2.00 cm?

(a) Calculate the density of a 374.5-g sample of copper if it has a volume of 41.8 cm3. (b) A student needs

15.0 g of ethanol for an experiment. If the density of ethanol is 0.789 g/mL, how many milliliters of ethanol

are needed? (c) What is the mass, in grams, of 25.0 mL of mercury (density = 13.6 g/mL)? Answer:


Sample Exercise 1.4 Determining Density and Using Density to Determine

Volume or Mass

Solution

(a) We are given mass and volume, so

Equation 1.3 yields

(b) Solving Equation 1.3 for volume and then

using the given mass and density gives

(c) We can calculate the mass from the

volume of the cube and its density. The

volume of a cube is given by its length cubed:

Solving Equation 1.3 for mass and

substituting the volume and density of the

cube, we have







Significant Figures

• The term significant figures refers to digits that were

measured.

• When rounding calculated numbers, we pay attention to

significant figures so we do not overstate the accuracy of

our answers.

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Significant Figures

1. All nonzero digits are significant.

2. Zeroes between two significant figures are

themselves significant.

3. Zeroes at the beginning of a number are never

significant.

4. Zeroes at the end of a number are significant if a

decimal point is written in the number.

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Hall, Inc.







Significant Figures

• When addition or subtraction is performed, answers are rounded to the least significant decimal place.

• When multiplication or division is performed, answers are rounded to the number of digits that corresponds to the least number of significant figures in any of the numbers used in the calculation.

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Accuracy versus Precision

• Accuracy refers to the proximity of

a measurement to the true value of

a quantity.

• Precision refers to the proximity of

several measurements to each

other.

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Hall, Inc.







Sample Exercise 1.5 Relating Significant Figures to the Uncertainty of a

Measurement

What difference exists between the measured values 4.0 g and 4.00 g?

A balance has a precision of ± 0.001 g. A sample that has a mass of about 25 g is placed on this balance. How

many significant figures should be reported for this measurement? Answer:


Solution

Many people would say there is no difference, but a scientist would note the difference in the number of

significant figures in the two measurements. The value 4.0 has two significant figures, while 4.00 has three.

This difference implies that the first measurement has more uncertainty. Amass of 4.0 g indicates that the

uncertainty is in the first decimal place of the measurement. Thus, the mass might be anything between 3.9

and 4.1 g, which we can represent as 4.0 ± 0.1 g. A measurement of 4.00 g implies that the uncertainty is in

the second decimal place. Thus, the mass might be anything between 3.99 and 4.01 g, which we can

represent as 4.00 ± 0.01 g. Without further information, we cannot be sure whether the difference in

uncertainties of the two measurements reflects the precision or accuracy of the measurement.







Sample Exercise 1.6 Determining the Number of Significant Figures in a

Measurement

How many significant figures are in each of the following numbers (assume that each

number is a measured quantity): (a) 4.003, (b) 6.023 1023, (c) 5000?

How many significant figures are in each of the following measurements:

(a) 3.549 g, (b) 2.3 104 cm, (c) 0.00134 m3? Answer:


Solution

(a) Four; the zeros are significant figures. (b) Four; the exponential term does not add to the number of

significant figures. (c) One. We assume that the zeros are not significant when there is no decimal point

shown. If the number has more significant figures, a decimal point should be employed or the number

written in exponential notation. Thus, 5000. has four significant figures, whereas 5.00 103 has three.







Sample Exercise 1.7 Determining the Number of Significant figures in a

Calculated Quantity

The width, length, and height of a small box are 15.5 cm, 27.3 cm, and 5.4 cm, respectively. Calculate the

volume of the box, using the correct number of significant figures in your answer.

It takes 10.5 s for a sprinter to run 100.00 m. Calculate the average speed of the sprinter in meters per second,

and express the result to the correct number of significant figures. Answer:


Solution

(The product of the width, length, and height determines the volume of a box. In reporting the product, we

can show only as many significant figures as given in the dimension with the fewest significant figures, that

for the height (two significant figures):

When we use a calculator to do this calculation, the display shows 2285.01, which we must round off to two

significant figures. Because the resulting number is 2300, it is best reported in exponential notation,

2.3 × 103, to clearly indicate two significant figures.








Calculated Quantity

A gas at 25 °C fills a container whose volume is 1.05 103 cm3. The container plus gas have a mass of

837.6 g. The container, when emptied of all gas, has a mass of 836.2 g. What is the density of the gas

at 25 °C?

Solution

To calculate the density, we must know both the mass and the

volume of the gas. The mass of the gas is just the difference in

the masses of the full and empty container: (837.6 – 836.2) g = 1.4 g

In subtracting numbers, we determine the number of significant figures in our result by counting decimal

places in each quantity. In this case each quantity has one decimal place. Thus, the mass of the gas, 1.4 g,

has one decimal place.

Using the volume given in the question, 1.05 103 cm3, and

the definition of density, we have

In dividing numbers, we determine the number of significant figures in our result by counting the number of

significant figures in each quantity. There are two significant figures in our answer, corresponding to the

smaller number of significant figures in the two numbers that form the ratio. Notice that in this example,

following the rules for determining significant figures gives an answer containing only two significant

figures, even though each of the measured quantities contained at least three significant figures.







To how many significant figures should the mass of the container be measured (with and without the gas) in

Sample Exercise 1.8 for the density to be calculated to three significant figures?

Answer:



Calculated Quantity







Dimensional Analysis

• We use dimensional analysis

to convert one quantity to

another.

• Most commonly dimensional

analysis utilizes conversion

factors (e.g., 1 in. = 2.54 cm)

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1 in.

2.54 cm

2.54 cm

1 in.

or








Use the form of the conversion factor that puts the

sought-for unit in the numerator.

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Hall, Inc.

Given unit desired unit

desired unit

given unit

Conversion factor








• For example, to convert 8.00 m to inches,

• convert m to cm

• convert cm to in.

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Hall, Inc.

8.00 m

100 cm

1 m

1 in.

2.54 cm

315 in.







Sample Exercise 1.9 Converting Units

If a woman has a mass of 115 lb, what is her mass in grams? (Use the relationships between

units given on the back inside cover of the text.)

By using a conversion factor from the back inside cover, determine the length in kilometers of a 500.0-mi

automobile race.

Answer:


Solution

Because we want to change from lb to g, we look for a relationship between these units of mass. From the

back inside cover we have 1 lb = 453.6 g. To cancel pounds and leave grams, we write the conversion factor

with grams in the numerator an pounds in the denominator:

The answer can be given to only three significant figures, the number of significant figures in 115 lb.







Sample Exercise 1.10 Converting Units Using Two or More Conversion Factors

The average speed of a nitrogen molecule in air at 25 °C is 515 m/s. Convert this speed to miles per hour.

Solution

To go from the given units, m/s, to the desired units, mi/hr, we must convert meters to miles and seconds to

hours. From our knowledge of metric prefixes we know that 1 km = 103 m. From the relationships given on

the back inside cover of the book, we find that 1 mi = 1.6093 km. Thus, we can convert m to km and then

convert km to mi. From our knowledge of time we know that 60 s = 1 min and 60 min = 1 hr. Thus, we can

convert s to min and then convert min to hr. Applying first the conversions for distance and then those for

time, we can set up one long equation in which unwanted units are canceled:

Our answer has the desired units. We can check our calculation, using the estimating procedure described in

the previous “Strategies” box. The given speed is about 500 m/s. Dividing by 1000 converts m to km, giving

0.5 km/s. Because 1 mi is about 1.6 km, this speed corresponds to 0.5/1.6 = 0.3 mi/s. Multiplying by 60

gives about 0.3 60 = 20 mi/min. Multiplying again by 60 gives 20 60 = 1200 mi/hr. The approximate

solution and the detailed solution are reasonably close. The answer to the detailed solution has three

significant figures, corresponding to the number of significant figures in the given speed in m/s.







Sample Exercise 1.10 Converting Units Using Two or More Conversion Factors

A car travels 28 mi per gallon of gasoline. How many kilometers per liter will it go?

Answer:








Sample Exercise 1.11 Converting Volume Units

Earth’s oceans contain approximately 1.36 109 km3 of water. Calculate the volume in liters.

If the volume of an object is reported as 5.0 ft3, what is the volume in cubic meters?

Answer:


Solution

This problem involves conversion of km3 to L. From the back inside cover of the text we find 1 L = 10–3 m3,

but there is no relationship listed involving km3. From our knowledge of metric prefixes, however, we have

1 km = 103 m and we can use this relationship between lengths to write the desired conversion factor

between volumes:

Thus, converting from km3 to m3 to L, we have







Sample Exercise 1.12 Conversions Involving Density

What is the mass in grams of 1.00 gal of water? The density of water is 1.00 g/mL.

Solution

1. We are given 1.00 gal of water (the known, or given, quantity) and asked to calculate its mass in grams

(the unknown).

2. We have the following conversion factors either given, commonly known, or available on the back inside

cover of the text:

The first of these conversion factors must be used as written (with grams in the numerator) to give the

desired result, whereas the last conversion factor must be inverted in order to cancel gallons:

The units of our final answer are appropriate, and we’ve also taken care of our significant figures. We can

further check our calculation by the estimation procedure. We can round 1.057 off to 1. Focusing on the

numbers that do not equal 1 then gives merely 4 1000 = 4000 g, in agreement with the detailed

calculation.







Sample Exercise 1.12 Conversions Involving Density

The density of benzene is 0.879 g/mL. Calculate the mass in grams of 1.00 qt of benzene.

Answer:


Solution (continued)

In cases such as this you may also be able to use common sense to assess the reasonableness of your answer.

In this case we know that most people can lift a gallon of milk with one hand, although it would be tiring to

carry it around all day. Milk is mostly water and will have a density that is not too different than water.

Therefore, we might estimate that in familiar units a gallon of water would have mass that was more than 5

lbs but less than 50 lbs. The mass we have calculated is 3.78 kg × 2.2 lb/kg = 8.3 lbs—an answer that is

reasonable at least as an order of magnitude estimate.

Documents

Study guide for AP test on TOPIC 1 Matter & Measurementtoolbox1.s3-website-us-west-2.amazonaws.com/site_0303/Lassiter_… · (b) Express the measurement 6.0 310 m using a prefix to